Multiple antennas employed at the transmitter and receiver can significantly increase the system capacity. By transmitting independent symbol streams in the same frequency bandwidth, usually termed as Spatial Multiplexing, SM, a linear increase in data rates with the increased number of antennas is achieved. On the other hand, by using space-time codes at the transmitter, reliability of the detected symbols can be improved by exploiting the so-called transmit diversity. Both these schemes assume no channel knowledge at the transmitter. However, in a practical wireless systems such as the 3rd Generation Partnership Project, 3GPP, Long Term Evolution, LTE, High Speed Downlink Packet Access, HSDPA, and Worldwide Interoperability for Microwave Access, WiMAX systems, the channel knowledge can be made available at the transmitter via feedback from the receiver to the transmitter. The MIMO transmitter may utilize this channel information to improve the system performance with the aid of precoding. In addition to beam forming gain, the use of precoding avoids the problem of ill-conditioned channel matrix.
In practice, complete Channel State Information, CSI, may be available for a communication system using the Time Division Duplex, TDD, scheme by exploiting channel reciprocity. However, for a Frequency Division Duplex, FDD, system, complete CSI is more difficult to obtain. In a FDD system, some kind of CSI knowledge may be available at the transmitter via feedback from the receiver. These systems are called limited feedback systems. There are many implementations of limited feedback systems such as e.g. codebook based feedback and quantized channel feedback. 3GPP LTE, HSDPA and WiMAX recommend codebook based feedback CSI for precoding.
In a codebook based precoding, a predefined codebook is defined both at the transmitter and at the receiver. The entries of codebook may be constructed using different methods. For example Grassmannian, Lloyd algorithm, Discrete Fourier Transform, DFT, matrix etc. The precoder matrix may be chosen to match the characteristics of the NR×NT MIMO channel matrix H, resulting in so-called channel dependent precoding. Here, NR represents the number of receive antennas and NT represents the number of transmit antennas, This is also commonly referred to as closed-loop precoding and essentially strives to focus the transmit energy into a subspace which is strong in the sense of conveying much of the transmitted energy to the UE.
In addition, the precoder matrix may also be selected to strive for orthogonalising the channel, meaning that after proper linear equalisation at the UE, the inter-layer interference is reduced. At the receiver it is common to find the Signal Interference Noise Ratio, SINR, with different codebook entries and choose the Rank/precoding index which gives highest spectral efficiency (capacity).
The performance of closed loop MIMO system generally improves with the cardinality (size) of the codebook set. At the receiver, Rank information and precoding index has to be sent back to the transmitter every TTI or multiples of TTI. In general, finding the Rank information and precoding index is cumbersome and involves many computations. Note that for a 4×4 MIMO system, the 3GPP standard specifies a codebook of 64 elements (16 codewords per each Rank)